The homotopy analysis method for q-difference equations

AbstractThe q-difference equations are kind of important problems in q-calculus and applied mathematics. In this paper, the homotopy analysis method is extended to find approximate solution for some of q-differential equations. The q-diffusion equation and some examples are analytically investigated. The series solutions obtained by the proposed method are checked by reducing the solutions of q-calculus problems to h-calculus approximate solutions when q→1

Satellite applications to marine geodesy

Potential use of satellites for enhancing positioning capabilities and for marine geodetic contro

Mass – Radius Relationship in Extrasolar Planets

The increasing number of Extrasolar planets observed in the last years makes important to define, as soon as possible, a mass – radius relationship, and so, we adjusted an planetary constitution independent experimental equation. Using the latest database of Extrasolar planets, a bi-logarithmic graphic was plotted that represents the mass - radius relationship where we adjusted a polynomial equation, which better suited the sample of Extrasolar planets at current time

On the first order operators in bimodules

We analyse the structure of the first order operators in bimodules introduced by A. Connes. We apply this analysis to the theory of connections on bimodules generalizing thereby several proposals.Comment: 13 pages, AMSLaTe

Theory of band gap bowing of disordered substitutional II-VI and III-V semiconductor alloys

For a wide class of technologically relevant compound III-V and II-VI semiconductor materials AC and BC mixed crystals (alloys) of the type A(x)B(1-x)C can be realized. As the electronic properties like the bulk band gap vary continuously with x, any band gap in between that of the pure AC and BC systems can be obtained by choosing the appropriate concentration x, granted that the respective ratio is miscible and thermodynamically stable. In most cases the band gap does not vary linearly with x, but a pronounced bowing behavior as a function of the concentration is observed. In this paper we show that the electronic properties of such A(x)B(1-x)C semiconductors and, in particular, the band gap bowing can well be described and understood starting from empirical tight binding models for the pure AC and BC systems. The electronic properties of the A(x)B(1-x)C system can be described by choosing the tight-binding parameters of the AC or BC system with probabilities x and 1-x, respectively. We demonstrate this by exact diagonalization of finite but large supercells and by means of calculations within the established coherent potential approximation (CPA). We apply this treatment to the II-VI system Cd(x)Zn(1-x)Se, to the III-V system In(x)Ga(1-x)As and to the III-nitride system Ga(x)Al(1-x)N.Comment: 14 pages, 10 figure

The SO(N) principal chiral field on a half-line

We investigate the integrability of the SO(N) principal chiral model on a half-line, and find that mixed Dirichlet/Neumann boundary conditions (as well as pure Dirichlet or Neumann) lead to infinitely many conserved charges classically in involution. We use an anomaly-counting method to show that at least one non-trivial example survives quantization, compare our results with the proposed reflection matrices, and, based on these, make some preliminary remarks about expected boundary bound-states.Comment: 7 pages, Late

High Time for Conservation: Adding the Environment to the Debate on Marijuana Liberalization

The liberalization of marijuana policies, including the legalization of medical and recreational marijuana, is sweeping the United States and other countries. Marijuana cultivation can have significant negative collateral effects on the environment that are often unknown or overlooked. Focusing on the state of California, where by some estimates 60% -- 70% of the marijuana consumed in the United States is grown, we argue that (a) the environmental harm caused by marijuana cultivation merits a direct policy response, (b) current approaches to governing the environmental effects are inadequate, and (c) neglecting discussion of the environmental impacts of cultivation when shaping future marijuana use and possession policies represents a missed opportunity to reduce, regulate, and mitigate environmental harm

Solutions of multigravity theories and discretized brane worlds

We determine solutions to 5D Einstein gravity with a discrete fifth dimension. The properties of the solutions depend on the discretization scheme we use and some of them have no continuum counterpart. In particular, we find that the neglect of the lapse field (along the discretized direction) gives rise to Randall-Sundrum type metric with a negative tension brane. However, no brane source is required. We show that this result is robust under changes in the discretization scheme. The inclusion of the lapse field gives rise to solutions whose continuum limit is gauge fixed by the discretization scheme. We find however one particular scheme which leads to an undetermined lapse reflecting the reparametrization invariance of the continuum theory. We also find other solutions, with no continuum counterpart with changes in the metric signature or avoidance of singularity. We show that the models allow a continuous mass spectrum for the gravitons with an effective 4D interaction at small scales. We also discuss some cosmological solutions.Comment: 19 page